Every time I take the rechargeable DeWalt drill off the shelf it has a dead battery and the spare is dead, too. So, is it OK to leave one battery on the charger when not in use?

I don't know if it's OK but I always leave one in the charger. Over the years, all my 18volt DeWalt ni-cads died, had about a half dozen. DeWalt now sells a lithium 20volt adapter kit, p/n DCA1820. It fits any DeWalt 18volt tool and it's a big improvement in performance. I bought the kit and tossed all the old ni-cads.

All my DeWalt tools are the 20v Lithium. batteries seem to last forever between charges. Just added a 1/2" impact to the set.

https://www.dewalt.com/dewalt-dna/fe...r-battery-life
DOES IT HURT DEWALT BATTERIES TO LEAVE THEM IN THE CHARGER? No. The DEWALT chargers have a maintenance mode which allows batteries to remain in the charger, maintaining a fully charged pack until the user is ready to work. ... Storing DEWALT Lithium Ion batteries outside of the charger will not result in loss of charge.

If DEWALT NiCd batteries are stored outside of the charger, they will discharge naturally, 15-20% the first 24 hours, 7-10% the next day, and about 1% every day there after. NiCd batteries lose the bulk of the capacity when outside of the charger in the first 3 days. In fact, it is better for the battery to leave it in the charger to be sure it goes through Equalization and Maintenance Modes